Explaining, convincing and proving

Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.

This article invites you to get familiar with a strategic game called "sprouts". The game is simple enough for younger children to understand, and has also provided experienced mathematicians with significant food for thought.

Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.

A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.

What does logic mean to us and is that different to mathematical logic? We will explore these questions in this article.

This article for pupils and teachers looks at a number that even the great mathematician, Pythagoras, found terrifying.

Proof does have a place in Primary mathematics classrooms, we just need to be clear about what we mean by proof at this level.

An introduction to proof by contradiction, a powerful method of mathematical proof.

The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!